| 书目名称 | Differential Geometry | | 副标题 | Connections, Curvatu | | 编辑 | Loring W. Tu | | 视频video | | | 概述 | Narrative provides a panorma of some of the high points in the history of differential geometry.Problems are presented in each chapter with selected solutions and hints given at the end of the book.Ac | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | This text presents a graduate-level introduction to differential geometry for mathematics and physics students. The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss‘ Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text..Prerequisite material is contained in author‘s text .An Introduction to Manifolds., and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions | | 出版日期 | Textbook 2017 | | 关键词 | Christoffel symbols; Codazzi–Mainardi equation; Gauss Curvature equation; Gauss Theorema egregium; Gauss | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-55084-8 | | isbn_softcover | 978-3-319-85562-2 | | isbn_ebook | 978-3-319-55084-8Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer International Publishing AG 2017 |
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发表于 2025-3-21 16:43:34
